Average Error: 32.0 → 0
Time: 8.5s
Precision: 64
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]
↓
\[1 - \frac{\left|x\right|}{x}\]
\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
1 - \frac{\left|x\right|}{x}
double f(double x) {
        double r4981317 = x;
        double r4981318 = r4981317 / r4981317;
        double r4981319 = 1.0;
        double r4981320 = r4981319 / r4981317;
        double r4981321 = r4981317 * r4981317;
        double r4981322 = sqrt(r4981321);
        double r4981323 = r4981320 * r4981322;
        double r4981324 = r4981318 - r4981323;
        return r4981324;
}
↓
double f(double x) {
        double r4981325 = 1.0;
        double r4981326 = x;
        double r4981327 = fabs(r4981326);
        double r4981328 = r4981327 / r4981326;
        double r4981329 = r4981325 - r4981328;
        return r4981329;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.0
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x \lt 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Derivation

  1. Initial program 32.0

    \[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]

  2. Simplified0

    \[\leadsto \color{blue}{1 - \frac{\left|x\right|}{x}}\]

  3. Final simplification0

    \[\leadsto 1 - \frac{\left|x\right|}{x}\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

  :herbie-target
  (if (< x 0) 2 0)

  (- (/ x x) (* (/ 1 x) (sqrt (* x x)))))